(a) The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 10 m/s.
(b) The velocity and acceleration at any time t is v = (2ati + bj) m/s and a = 2ai m/s²
(c) The average acceleration in the time interval given in part (a) is 4 m/s².
Position of the particlex = at²i + btj
x = 2t²i + tj
Average velocity, at t₁=2sec and t₂=3secΔv = Δx/Δt
x(2) = 2(2)²i + 2j
x(2) = 8i + 2j
|x(2)| = √(8² + 2²) = 8.246
x(3) = 2(3)²i + 3j
x(3) = 18i + 3j
|x(3)| = √(18² + 3²) = 18.248
Δv = (18.248 - 8.246)/(3 - 2)
Δv = 10 m/s
Velocity and acceleration at any time, tx = at²i + btj
v = dx/dt
v = (2ati + bj) m/s
a = dv/dt
a = 2ai m/s²
Average accelerationa = 2ai m/s²
a = 2(2)(1)
a = 4 m/s²
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what will happen to the pressure in a gas if you compressed it into a volume that was one third the size? why?
Answer:
Pressure will triple (Boyle's Law)
Explanation:
Assuming a constant temperature: (compressing gases usually raises the temp significantly):
P1V1 = P2V2
P1V1 / V2 = P2
Now change V2 to 1/3 V2:
P1V1 / (1/3 V2 ) = P2 / (1/3 )
P1V1/ (1/3 v2 ) = 3 P2 <======= THE PRESSURE WILL TRIPLE
This is Boyle's Law
Question 3 of 15
Which statement describes an advantage of using nuclear fission to produce
electricity?
A. It uses a fuel made of atoms with large nuclei that will be
destroyed.
B. It is much more efficient than any other process used to generate
power.
C. It happens in large buildings that are expensive to build.
D. It produces radioactive waste products that must be stored safely.
Answer:
it is much more efficient than any other process to generate power
I was having trouble converting this p-t graph into a velocity-time graph and acceleration-time graph. Can someone convert it and send a picture of it?
We can obtain the velocity from the graph and plot is against time to obtain a velocity time graph.
What is a velocity time graph?The velocity time graph shows the change of velocity with time. Recall that velocity is the change of position with time.
As such, when we have a position time graph as shown, we can obtain the velocity from the graph and plot is against time to obtain a velocity time graph.
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There are space stations Alpha and Beta located on the line between the planets. Both space stations are at rest with respect to the planets. Alpha is at distance d 4 from planet 1 and Beta is at distance d 3 from planet 2. A projectile of mass m is fired from station Alpha, with its velocity v pointing directly at planet 2. What is the minimum speed v which will permit the projectile to reach station Beta?
The minimum speed v which will permit the projectile to reach station Beta is √ [Gm/3d]
What is gravitational potential energy?If an object is lifted, work is done against gravitational force. The object gains energy.
Given are space stations Alpha and Beta located on the line between the planets. Both space stations are at rest with respect to the planets. Alpha is at distance d 4 from planet 1 and Beta is at distance d 3 from planet 2. A projectile of mass m is fired from station Alpha, with its velocity v pointing directly at planet 2.
The range of the projectile is given by R = v²sin2θ / g
g = gravitational acceleration of Earth
If g = g(p) for planet , range R = v²sin2θ / g(p)..................(1)
The gravitational force of attraction = weight force
Gm² /d² = m g(p)
g(p) = Gm/d².........................(2)
For R = d/3, from equation (1), we have
d/3 = v²sin2θ / g(p)
Plug the expression for g(p) , we get
v = √ [Gm/3dsin2θ ]
For velocity to be minimum, sin2θ =1
So, the minimum velocity will be
v = √ [Gm/3d]
Thus, the minimum speed v which will permit the projectile to reach station Beta is √ [Gm/3d]
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A long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is λ = a[tex]x^{3}[/tex] + bx, where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/[tex]m^{4}[/tex] and b = 2.20 kg/[tex]m^{2}[/tex].
1. Determine the total mass of the rod.
2. Calculate the x-coordinate of the center of the mass for this rod.
1. The total mass of the rod is 61.48 kg.
2. The x-coordinate of the center of the mass for this rod is 172.6021 m.
What is density?The density is the ratio of the mass and the volume of the object. It is denoted by ρ.
ρ = mass/Volume = m/V
Given a long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is
λ = ax³ + bx,
where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/m⁴ and b = 2.20 kg/m²
So, λ = 1.70x³ + 2.20x
1. The total mass of the rod is
m =₁.₈³⁴ ∫ [1.70x³ + 2.20x] dx
m = [ 1.70x⁴/4 + 2.20x² /2 ]₁.₈³⁴
Putting the limits, we have
m = 69.51 - 8.02548
m = 61.48 kg
Thus, the total mass of the rod is 61.48 kg
2. The x-coordinate of the center of the mass for this rod
Xcm =∫ xλdx/m
Xcm =∫[ x ( 1.70x³ + 2.20x) /m ]dx
Xcm =∫[( 1.70x⁴ + 2.20x²) /m ]dx
On integrating and putting the limits x = 1.80 m to x = 3.40 m
Xcm = = [ {1.70(3.4)⁵/5 + 2.20(3.4)³ /3} - {1.70(1.8)⁵/5 + 2.20(1.8)³ /3} ]
Xcm = 183.3034 - 10.70133
Xcm = 172.6021 m
Thus, the x-coordinate of the center of the mass for this rod is 172.6021 m.
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What is the speed of a 16 cm wave with a period of 8 seconds?
A) 48 cm/s
B) 0.5 cm/s
C) 200 cm/s
D) 2 cm/s
The speed of a 16cm wave with a period of 8 seconds is 2cm/s
How to determine the speedUsing the formula;
Speed = distance ÷ time
Distance = 16cm
time = 8 seconds
Substitute into the formula
Speed = 16 ÷ 8
Speed = 2 cm/s
Therefore, the speed of a 16cm wave with a period of 8 seconds is 2cm/s
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find the direction of this vector.
The direction of this vector is 170° from the positive x-axis.
Vectors are physical quantities with both magnitude and directionTo identify the direction, we usually use angles and take a reference axisThe vector in the diagram is 80° to the left of the positive y-axis, so the direction of the vector is 80° + 90° = 170° anti-clockwise from the positive x-axis.Scalars are physical quantities which have only magnitudeExamples of vector quantities are displacement, velocity, acceleration, force etcExamples of scalar quantities are distance, speed, volume, density, mass, time etcThe direction of the given vector is 170° from the positive x-axis.Learn more about vectors here:
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According to the __________perspective, people who suffer from PTSD are classically conditioned.
According to the pavlovian perspective, people who suffer from PTSD are classically conditioned.
What is PSTD?
This is referred to as post traumatic stress disorder which is a mental disorder from a terrifying incident.
The pavlovian perspective however view this disorder as being a type of classical conditioned one.
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A periodic wave has a wavelength of 0,50 m and a speed of 20 m/s, What is the wave frequency?
Answer:
u=speed, w=wavelenght, f=frequency
It's known that u=w*f => f=u/w
u=20m/s ==> f=20/0,5 => f=40 Hz
w=0,50m
Explanation:
differentiate e^x - 8x +7
please answer the questions asap
Answer:
eˣ-8.
Explanation:
(eˣ-8x+7)'=eˣ-8.
If the mass of the falling object is 60kg. Calculate force. [Take g=10m/s2]
C1=10 μF , C2= 50 μF, C3=9 μF, C4=2 μF, C5= 0.1 μF
What is the equivalent capacitance of these capacitors as they are arranged?
The equivalent capacitance of these capacitors as they are arranged in series and parallel will be 0.093 μF and 71.1 μF.
What is a capacitor?A capacitor is a device that can store electrical energy. It is a two-conductor configuration separated by an insulating medium that carries charges of equal size and opposite sign.
If the capacitor is connected in the series the equivalent capacitance is found as;
[tex]\rm \frac{1}{c_{eq}} = \frac{1}{c_1} +\frac{1}{c_2} +\frac{1}{c_3} +\frac{1}{c_4} +\frac{1}{c_5} \\\\\ \rm \frac{1}{c_{eq}} = \frac{1}{10} +\frac{1}{50} +\frac{1}{9} +\frac{1}{2} +\frac{1}{0.1} \\\\\ \frac{1}{c_{eq}} = 0.1+0.02+0.11+0.5+10 \\\\ \frac{1}{c_{eq}} = 10.7 \\\\ c_{eq} = 0.093 \ \mu F[/tex]
If the capacitor is connected in parallel the equivalent capacitance,cₐ is found as;
cₐ= c₁+c₂+c₃+c₄+c₅
cₐ = 10+50+9+2+0.1 μF
cₐ =71.1 μF
Hence, the equivalent capacitance of these capacitors as they are arranged in series and parallel will be 0.093 μF and 71.1 μF.
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What is the effect on a field of tall grass when a wave caused by a cool summer breeze passes through the field?
Select one:
a. The grass leans in the direction the wind is blowing, then returns to its original position.
b. The field of grass exhibits a permanent disturbance in the direction the wind is blowing.
c. To counteract the effect of the breeze, the grass leans into the wind.
d. Some grass leans in the direction the wind is blowing and some leans into the wind.
Whenever a wave is brought on by a cool summer breeze across the field. The grass tilts in the wind's direction before reverting to its original posture. Option A is correct.
What is the wind blowing?Air pressure variations within our atmosphere result in the wind, which is the movement of air.
Areas with a low pressure are approached by air in high pressure. The air flows more quickly when there is a bigger pressure differential. Most rapid winds.
The wind is the movement of air produced by changes in air pressure in our atmosphere.
High-pressure air goes toward low-pressure locations. The bigger the pressure differential, the faster the air moves.
Hence, option A is correct.
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An electric field is described by the vector e=yj -xi. what is the electric flux through a rectangular box in the x-z plane that is bounded by x between 0 and 1, and z between 0 and 1? (You need to identify dA to do this problem.)
The flux of [tex]\vec E = -x\,\vec\imath + y\,\vec\jmath[/tex] is given by the surface integral
[tex]\displaystyle \iint_S \vec E \cdot d\vec\sigma[/tex]
where [tex]S[/tex] is the given square region, which we can parameterize by
[tex]\vec s(x, z) = x\,\vec\imath + z\,\vec k[/tex]
with [tex]0\le x\le 1[/tex] and [tex]0\le z\le 1[/tex]. The area element is
[tex]d\vec\sigma = \vec n \, dx\,dz[/tex]
where [tex]\vec n[/tex] is the normal vector to [tex]S[/tex]. Depending on the orientation of [tex]S[/tex], this vector could be
[tex]\vec n = \dfrac{\partial\vec s}{\partial x} \times \dfrac{\partial\vec s}{\partial z} = -\vec\jmath[/tex]
or [tex]-\vec n = \vec \jmath[/tex]; either way, the integral reduces to
[tex]\displaystyle \iint_S \vec E \cdot d\,\vec\sigma = \int_0^1 \int_0^1 (-x\,\vec\imath + z\,\vec k) \cdot (\pm\vec\jmath) \, dx\,dz = \boxed{0}[/tex]
Which of the following best represents the energy transformations in an
electric motor?
A. Mechanical energy
in electromagnet
-
changing electric field -> electrical energy
B. Electrical energy in current → magnetic energy in electromagnet
OC. Electrical energy in current → changing magnetic field →
mechanical energy
-
OD. Mechanical energy → changing magnetic field → electrical
energy in current
The energy transformations in an electric motor are, electrical energy in current → changing magnetic field → mechanical energy. Option C is corect.
What is the law of conservation of energy?According to the law of conservation of energy, energy can neither be created nor destroyed, but it can be transferred from one form to another.
The total energy is the sum of all the energies present in the system. The potential energy in a system is due to its position in the system.
An electric motor is a mechanism that turns electricity into mechanical energy.
The interaction between the motor's magnetic field and electric current in a wire winding generates force in the form of torque imparted to the motor's shaft in most electric motors.
An electric generator is physically equivalent to an electric motor, but it converts mechanical energy into electrical energy using a reversed flow of power.
In an electric motor, energy is transformed into mechanical energy, electrical energy in current, and changing magnetic energy.
The energy transformations in an electric motor are;
Electrical energy in current → changing magnetic field → mechanical energy.
Hence option C is correct.
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A satellite completes one revolution of a planet in almost exactly one hour. At the end of one hour, the satellite has traveled 2.0 × 107 meters and is only 10 meters away from its starting point. What is the numerical value of the satellite's average velocity after that one hour?
Answer:
shown below
Explanation:
2 x 10⁷ as a number is 20,000,000
20,000,000 - 10 = 19,999,990
It went 19,999,990 m/h
in km/h:
19,999,990 / 1000 = 19,999.99 km/h
in km/s
19,999,990 / 3,600,000 = ~5.56 km/s
in m/s
19,999,990 / 3600 = ~5555.56 m/s
What is an advantage of using renewable energy resources?
A. They can be converted directly into electric energy.
B. They do not waste energy in heat.
C. They can be replenished in a human lifetime.
D. They do not produce greenhouse gases.
As you move down a period of the periodic table from top to bottom, what happens to the elements' electronegativity?
A.
It decreases.
B.
It changes in relation to the number of electrons.
C.
It changes in relation to the number of protons.
D.
It increases.
Answer:
A.) It decreases
Explanation:
Generally, as you go from the top to the bottom of the periodic table (down a column), the electronegativity values of the elements decrease.
Also, as you move to the right of the periodic table (across a period), the electronegative values increase. The most electronegative elements are located on the top-right of the periodic table.
What work do you think is done when you carry a 20 N weight backpack for a 1000 m walk? will the work be positive, negative, or potentially zero?
The work done is positive and is equal to 20000 J
What is work done?Work done is defined as the product of force and the distance moved by the force.
Mathematically:
Work done = force * distanceThe work done by the force = 20 * 1000 = 20000J
The work done is positive and is equal to 20000 J
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8. A charged ball of mass m = 0.265 kg and unknown charge q is hanging by a light thread from a ceiling. A fixed charge Q = +5.00 μC on an insulated stand is brought close to the unknown charge. As a result, the unknown charge hangs at an angle 0 = 38.0° to the vertical as shown in the diagram below. The distance between the two charges is r = 22.0 cm. (a) What is the sign of the unknown charge? Explain how you know this. (b) What is the magnitude of the unknown charge? 8. A charged ball of mass m = 0.265 kg and unknown charge q is hanging by a light thread from a ceiling . A fixed charge Q = +5.00 μC on an insulated stand is brought close to the unknown charge . As a result , the unknown charge hangs at an angle 0 = 38.0 ° to the vertical as shown in the diagram below . The distance between the two charges is r = 22.0 cm . ( a ) What is the sign of the unknown charge ? Explain how you know this . ( b ) What is the magnitude of the unknown charge ?
(a) The sign of the unknown charge is negative.
(b) The magnitude of the unknown charge is 2.18 μC.
What is charge?The charge is the physical quantity which defines the object's electric field. The charged objects creates the electric field around it and attracts or repels another objects coming into that field.
Given is a charged ball of mass m = 0.265 kg and unknown charge q is hanging by a light thread from a ceiling. A fixed charge Q = +5.00 μC on an insulated stand is brought close to the unknown charge. As a result, the unknown charge hangs at an angle 0 = 38.0° to the vertical as shown in the diagram below. The distance between the two charges is r = 22.0 cm.
Tension in the string has two components, Tsinθ and Tcosθ
(a) The fixed charge Q will attract the movable charge q attached to string. The charge Q is positive. So, the charges must of opposite sign.
Thus, the sign of unknown charge is negative.
(b) From the equilibrium of forces, we get
Electrostatic force Fe = kQq/r²
Fe = Tsinθ .............(1)
and
weight force mg = Tcosθ.............(2)
Dividing both the equations, we get
mg/Fe = tanθ
mg / (kQq/r²) = tanθ
q = mgr²tanθ / kQ
Substitute the values from the question, we have
q = 0.265 x 9.81 x (0.22)² tan38 / (9x10⁹ x 5 x 10⁻⁶)
q = 2.18 x 10⁻⁶ C
or q = 2.18 μC
Thus, the magnitude of charge is 2.18 μC.
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A plant is thrown straight
down from a balcony 7.01 m
high at 8.84 m/s. How long
does it take the plant to hit
the ground?
The time taken for the plant to hit the ground from a distance of 7.01m and at a velocity of 8.84m/s is 1.59s.
How to calculate time?The time taken for a motion to occur can be calculated using the following formula:
v² = u² - 2as
Where;
v = final velocityu = initial velocitys = distancea = acceleration8.84² = 0² + 2 × a × 7.01
78.15 = 14.02a
a = 5.57m/s²
V = u + at
8.84 = 0 + 5.57t
t = 1.59s
Therefore, the time taken for the plant to hit the ground from a distance of 7.01m and at a velocity of 8.84m/s is 1.59s.
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A comet goes around the sun in an elliptical orbit. At its farthest point, 455 million miles from the sun, it is traveling with a speed of 15,135 mi/h. How fast is it traveling at its closest approach to the sun, at a distance of 116 million miles?
Answer:
A 2kg block is moved a long a level floor by a horizontal force of 20N if the coefficient of sliding friction is 0.4
what is the acceleration of the blove
when energy is transferred from one part of a system to another, some of the energy is lost during the transfer and cannot be used as it was intended. Which two sentences describes examples of this?
Sentences A and D describe examples of energy transformation.Heat is produced when a car's tires rub against the pavement and as electricity passes across power wires, they become hotter.
What is the law of conservation of energy?According to the law of conservation of energy, the energy of an isolated system stays unchanged throughout time.it is said to be conserved.
Energy cannot be created nor destroyed and can be transferred from one form to the other form.
The complete question is
"When energy is moved from one component of a system to another, some of the energy is lost and cannot be used as planned.
Which two statements provide examples?
A. Friction between a car's tires and the road produces heat.
B. Sunlight strikes a solar panel, generating electricity.
c. Stereo speakers emit a sound when powered by electrical energy,
D. Wind moves a turbine, generating electricity.
I E. Power lines heat up as electricity flows through them."
Some of the energy wasted during the movement of energy from one section of a system to another is heat is produced by friction between a car's tires and the road and as electricity passes via power lines, they heat up.
Hence, sentences A and D describe examples of energy transformation.
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Which graph shows constant acceleration with correctly placed independent and dependent variables?
Answer:
a = (V2 - V1) / t equation for constant acceleration
if t the independent variable is placed on the abcissa or x-axis and V the dependent variable is placed on the ordinate or y-axis then the acceleration would be the slope at the point considered.
Calculate the magnitude of the linear momentum for the following cases.
(a) a proton with mass 1.67 x 10-27 kg, moving with a speed of 5.05 x 106 m/s
(d) the Earth (mass - 5.98 x 1024 kg) moving with an orbital speed equal to 2.98 x 10 m/s.
Answer:
8.4335 x 10^-²¹, 1.78204 x 10²⁶
Explanation:
p = mv
p = (5.05 x 10⁶)(1.67 x 10^-²⁷)
p = 8.4335 x 10^-²¹
p = mv
p = (5.98 x 10²⁴)(2.98 x 10)
p = 1.78204 x 10²⁶
a 10.00mf parallel-plate capacitor is connected to a 24.0v battery. after the capacitor is fully charged ,the
battery is disconnected without loss of any of charge on the plates.
a) a voltmeter is connected across the two plates without discharging them.what does it read
b)what would the voltmeter read if the plate separationwere doubled?
The answer to the first part of the question is 24 V and the answer to the second part of the question is 48 V.
The formula which relates Charge, Capacitance and Voltage is
Charge = Capacitance × Voltage
Q = CV
where Q denotes the charge, C denotes the capacitance and V denote the voltage.
Using the above formula the charge on the capacitance will be
Q = CV
C = 10 mF
V = 24 V
Q = 240 mC
Charge on capacitance is 240 mC.
Now after we disconnect the battery
C = 10 mF (will remain same)
Q = 240 mC
V = Q/C
V = 240/10 V
V = 24 V
So after we removed the battery, The voltage will remain same.
Now we know that parallel plate capacitor formula is
C = ε(A/d)
from here
C ∝ 1/d, and as there is no loss of charge we can say that V ∝ 1/d
Form C ∝ 1/d and V ∝ 1/C we can state that
V ∝ d {where d is the measurement of separation between the plates}
so if we double the distance between the plates then, the voltage will also get double.
Previously our voltage was 24 V, now if we double the distance between the plates the voltage will also get double, and it will become 48 V.
So, the voltmeter will take a reading of 24 V if voltmeter is connected across the two plates without discharging them, and if we double the plate separation then it will take 48 V as reading.
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Exam Which is a true statement about the energy level of gas? A. Gases have very little energy. B. Gases have more energy than liquids and solids. C. Gases have no energy. D. Gases have less energy than solids. Copyright © 2003-2022 International Academy of Science. All Rights Reserved. Exam Which is a true statement about the energy level of gas ? A. Gases have very little energy . B. Gases have more energy than liquids and solids . C. Gases have no energy . D. Gases have less energy than solids . Copyright © 2003-2022 International Academy of Science . All Rights Reserved .
Statement B is true about the energy level of gas, Gases have more energy than liquids and solids.
What is gas?A gas is a sample of matter that adopts the shape of the container in which it is housed and develops a uniform density inside the container.
Liquid molecules are more energetic than solid molecules. Further heating will cause the molecules to move so quickly that they won't stick together at all. The gas molecules have the highest energy content.
Gases have more energy than liquids and solids.
Hence statement B is true about the energy level of gas.
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an ac voltage of 12.0 v is applied to the primary transformer that has 3 times as many turns in the secondary than in the primary. what is the voltage of the secondary?
The voltage of the secondary will be 36 V.From the given conditions primary transformer has 3 times as many turns in the secondary coil.
What is induced voltage?Electromagnetic induction is what causes the induced voltage. Electromagnetic induction is the process of generating emf (induced voltage) by subjecting a conductor to a magnetic field.
In this case, a magnet is pushed in and out of a wire coil attached to a high-resistance voltmeter.
Typically, a transformer's primary winding is attached to the input voltage source and changes electrical power into a magnetic field.
The secondary winding's role is to turn this alternating magnetic field into electricity, generating the necessary output voltage.
Given data;
Primary coil voltage,[tex]\rm V_P = 12 \ v[/tex]
Secondary coil voltage,[tex]\rm V_s = ?[/tex]
No turns in the primary coil,[tex]\rm N_p[/tex]
No turns in the secondary coil,[tex]\rm N_s[/tex]
From the given condition;
[tex]\rm N_s = 3N_p[/tex]
For a transformer,
[tex]\rm \frac{V_p}{V_s}= \frac{N_p}{N_s} \\\\ \rm \frac{12}{V_s}= \frac{N_p.}{3N_p} \\\\ V_s = 36 \ V[/tex]
Hence the voltage of the secondary will be 36 V.
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A person lifts a ball of mass 1 kg through the
height of 1 m in 10 s. The average power
supplied by him is [Take g = 10 m/s²]
(2) 1 W
(4) 2 W
(1) 10 W
(3) 0.1 W
Answer:
1 W
Explanation:
Power is the ratio of the total work done by the body to the time it will takes to do the work.
Therefore Power = total work done ÷ timeTotal Work done = Potential energy (P.E) = mgh
Total work done = mgh
Total work done = 1kg × 10m/s² × 1m
Total work done = 10 J
Therefore Total Work done is 10J.
And then time is 10 s.
Power = Total Work done divided by time
Power = 10 J÷ 10 s = 1 W
Therefore Power is 1WHow to do projects on newton’s law
